On the structure of smooth components of Springer fibers

Lucas Fresse; Anna Melnikov; Sammar Sakas-Obeid

doi:10.1090/S0002-9939-2015-12460-4

On the structure of smooth components of Springer fibers

Lucas Fresse, Anna Melnikov, Sammar Sakas-Obeid

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The aim of this paper is to study the structure of the smooth irreducible components of the Springer fibers associated to nilpotent endomorphisms of nilpotency order 2. Relying on its combinatorial interpretation in terms of standard Young tableaux, we show that each smooth component has a structure of iterated bundle of Grassmannian varieties, with explicit base. Using this description, we then classify the smooth components according to their Poincaré polynomials.

Original language	English
Pages (from-to)	2301-2315
Number of pages	15
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9939-2015-12460-4
State	Published - 2015

Bibliographical note

Publisher Copyright:
© 2015 American Mathematical Society.

Keywords

Betti numbers
Components of a Springer fiber
Flag manifolds
Grassmannian varieties
Iterated bundles

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-2015-12460-4

Cite this

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KW - Flag manifolds

KW - Grassmannian varieties

KW - Iterated bundles

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On the structure of smooth components of Springer fibers

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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